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While deep neural networks provide good performance for a range ofchallenging tasks, calibration and uncertainty estimation remain majorchallenges, especially under distribution shift. In this paper, we propose theamortized conditional normalized maximum likelihood (ACNML) method as ascalable general-purpose approach for uncertainty estimation, calibration, andout-of-distribution robustness with deep networks. Our algorithm builds on theconditional normalized maximum likelihood (CNML) coding scheme, which hasminimax optimal properties according to the minimum description lengthprinciple, but is computationally intractable to evaluate exactly for all butthe simplest of model classes. We propose to use approximate Bayesian inferencetechnqiues to produce a tractable approximation to the CNML distribution. Ourapproach can be combined with any approximate inference algorithm that providestractable posterior densities over model parameters. We demonstrate that ACNMLcompares favorably to a number of prior techniques for uncertainty estimationin terms of calibration on out-of-distribution inputs.

Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation